Counting and sizing blood cells in hematological analyzers is achieved using the Coulter principle. The cells flow in a micro-aperture in which a strong electrical field is imposed, so that an electrical perturbation, called pulse, is measured each time a cell crosses the orifice. The pulses are expected to contain information on the shape and deformability of Red Blood Cells (RBCs), since recent studies state that RBCs rotate and deform in the micro-orifice. By implementing a dedicated numerical model, the present study sheds light on a variety of cells dynamics, which leads to different associated pulse signatures. Furthermore, simulations provide new insights on how RBCs shapes and mechanical properties affect the measured signals. Those numerical observations are confirmed by experimental assays. Finally, specific features are introduced for assessing the most relevant characteristics from the various pulse signatures and shown to highlight RBCs alterations induced by drugs. In summary, this study paves the way to a characterization of RBC rheology by routine hematological instruments.